Circle Tangent to Line
Date: 04/19/2001 at 17:25:36 From: Lewis Subject: Given 2 points and tangent, determine circle I've had trouble finding the circle that passes through two given points and is tangent to a line. Knowing where the circle touches the tangent has stumped me. I've drawn the perpendicular bisector between the points and the perpendicular from the tangent, but stop there.
Date: 04/19/2001 at 18:25:41 From: Doctor Jaffee Subject: Re: Given 2 points and tangent, determine circle Hi Lewis, You're almost there. The perpendicular bisector that you constructed between the two given points must pass through the center of the circle. Furthermore, the length of the segment that connects the tangent line and the perpendicular bisector must equal the length of the radius. So, set the radius of your compass equal to the length of the segment that connects the tangent line and the perpendicular bisector, and place the point of your compass on one of the given points. Where the arc crosses the perpendicular bisector will be the center of your circle. If you need an algebraic solution, you can use an analogous procedure. I hope this works for you. Let me know if you have any difficulties. - Doctor Jaffee, The Math Forum http://mathforum.org/dr.math/
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